This game, as with the rest of the Layton series, is very slow, quiet and cerebral. Many other titles boast "puzzle-solving", but the bulk of this game consists of puzzles in the traditional sense--straight brainteasers, logic puzzles and the odd bit of algebra. It's all presented entertainingly with an anime-style story and colorful, voice-acted characters, but most of your play time will be spent staring ponderously at a puzzle while the same (the same!) song loops. It's an experience most players will either adore or dislike almost immediately. I'm more of a right-brain creative type and found many of the puzzles too hard, but your mileage may vary.
This is the first 3DS entry in the series and I can't say I'm impressed. The earlier games' expressive 2D art has been replaced by somewhat chunky-looking 3D sprites with drawn-on flapping mouths and a limited range of motion. The anime cutscenes are gorgeous but the bulk of the story is told by these clunky puppets. Voice acting is generally good, though Layton's assistant Luke gets pretty shrill. Music is high-quality and pleasantly unobtrusive. Much of the dialogue is predictable and fairly unnecessary--in my first 40 minutes of play I solved only two puzzles and was only skimming the text. 3D is implemented reasonably well.
Bottom line: This is a fairly-long, quiet game that will appeal to logic-lovers. Newcomers to the series, rent before you buy.